In order to compute the area of a particular circle, Juan first measures the length of its diameter. The actual diameter is 20 cm, but Juan's measurement has an error of up to $20\%$. What is the largest possible percent error, in percent, in Juan's computed area of the circle?
Juan can measure the diameter as a length anywhere between $20 - 20\cdot 0.2 = 16$ and $20 + 20\cdot 0.2 = 24$  cm. The actual area of the circle is $\pi (20/2)^2=100\pi$ square cm, but Juan can compute the area anywhere in the range $\pi (16/2)^2=64 \pi$ square cm to $\pi (24/2)^2=144 \pi$ square cm. Using the lower bound of the range, Juan's error is $(100\pi - 64\pi)/(100\pi)=36\%$. Using the upper bound of the range, Juan's error is $(144\pi - 100\pi)/(100\pi)=44\%$. Thus, the largest possible percent error is $\boxed{44}$ percent.